There's also a plane made from a plain sheet of white paper. That one is Rare, because it includes the Shading Texture that will let you make your own paper plane from any image you like! (Instructions are included.)

The mesh is the same as the one that was in the gacha machine I had at The Arcade Gacha Festival from Sept. 15 to Oct. 15 this year. That design was exclusive to The Arcade though, so I'm sorry if you missed it. These are all totally different.